Is there a classification of real-linear (rather than complex-linear) finite-dimensional representations of SL(2,C)?
2026-05-05 23:21:47.1778023307
Real representations of SL(2,C)
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On the level of the Lie algebra, this is the same as the real representation theory of $SO(3,1)$. Theory of irreducible representations of simple real Lie algebras is well-developed, see for instance this book.